Method and apparatus for prediction of polishing condition, and computer product

ABSTRACT

A polishing-condition predicting apparatus determines optimum parameters to be substituted into various function models by performing calibration by use of a TEG. A polishing condition enabling polishing of a thin film formed on a substrate to be designed so as to obtain a desirable height of the thin film and a desirable depth of a groove is predicted by simulation using the determined optimum parameters.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority fromthe prior Japanese Patent Application No. 2006-246680, filed on Sep. 12,2006, the entire contents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a technology of prediction of apolishing condition on which a thin film on a semiconductor device ispolished.

2. Description of the Related Art

According to microfabrication and multiple layer wiring of asemiconductor device, flatness is required in each layer. Specifically,in terms of improvement of quality, it is important to polish a surfaceof a substrate on which copper plating or the like is applied, by achemical mechanical planarization (CMP) or the like, to obtain uniformflatness in a wiring process in semiconductor device fabrication.

A polishing condition is important to properly polish the copper platingformed on the substrate. The polishing condition should vary accordingto the thickness of the copper plating. Specifically, the polishingcondition is determined based on the combination of a polishing time, apolishing pressure, and a polishing rotational speed when the copperplating is polished by a polishing pad, for example.

A polishing condition for copper plating formed on a substrate isconventionally determined by using a test substrate called a testelement group (TEG). For example, the TEG is polished at a certainpolishing rotational speed under a certain polishing pressure, and then,the height of the copper plating formed on the substrate and the unevendepth of the copper plating are measured.

Next, calibration is carried out based on the measurement result, andthen, a parameter of a simulation model in polishing prediction isextracted. A polishing condition is determined by carrying out apolishing prediction simulation by using the extracted parameter (forexample, Japanese Patent Application Laid-open No. 2004-516680).

However, a series of operations are required to be repeated when thepolishing pressure and the polishing rotational speed during thepolishing are changed in the TEG measurement by the above conventionaltechnique. Therefore, it requires much working time for searching anoptimum polishing condition, thereby increasing the design period andlabor.

An optimum polishing condition may be searched by changing only thepolishing time. However, it is difficult to optimize both of the heightof the copper plating formed on the substrate and the groove depth ofthe copper plating at the same time, thereby making it impossible toestablish the optimum polishing condition.

As a result, the substrate cannot be planarized, and therefore, a shortis caused in the wiring due to contact of wirings or a focus isinconveniently shifted in forming a wiring pattern, thereby reducing theyield.

SUMMARY OF THE INVENTION

It is an object of the present invention to at least solve the aboveinvention.

A computer-readable recording medium according to one aspect of thepresent invention stores therein a polishing-condition predictingprogram for predicting a polishing condition by using a test substratehaving a wiring groove formed in a predetermined shape, the polishingcondition in polishing a thin film formed on a substrate by a polisher.The polishing-condition predicting program includes receiving a possiblevalue of parameters of a wiring width in a region of interest on a thinfilm formed on the test substrate, the parameter values included in agroove depth function model expressing a maximum depth at which apolisher enters into the groove in the region; calculating a depth modelvalue expressing a depth at which the polisher enters into the groove inthe region and an adjacent region thereof by substituting the possibleparameter and dimensional data of the wiring width into the groove depthfunction model; calculating a pressure to be applied to the region bysubstituting the model values of the region and the adjacent region intoa pressure function model expressing pressure by height of the thin filmin each region; calculating thickness of the thin film in the regionafter the polishing by substituting the calculated pressure into a speedfunction model expressing a polishing speed; calculating a differencebetween the calculated thickness and an actual thickness of the thinfilm measured in the region after the polishing; and determining anoptimum value for the parameters of the wiring width based on a resultof calculation at the calculating a difference.

A polishing-condition predicting apparatus according to another aspectof the present invention predicts a polishing condition by using a testsubstrate having a wiring groove formed in a predetermined shape, thepolishing condition in polishing a thin film formed on a substrate by apolisher. The polishing-condition predicting apparatus includes areceiving unit that receives a possible value of parameters of a wiringwidth in a region of interest on a thin film formed on the testsubstrate, the parameter values included in a groove depth functionmodel expressing a maximum depth at which a polisher enters into thegroove in the region; a depth calculating unit that substitutes thepossible parameter and dimensional data of the wiring width into thegroove depth function model, to calculate a model value expressing adepth at which the polisher enters into the groove in the region and anadjacent region thereof; a pressure calculating unit that substitutesthe model values of the region and the adjacent region into a pressurefunction model expressing pressure by height of the thin film in eachregion, to calculate a pressure to be applied to the region; a thicknesscalculating unit that substitutes the calculated pressure into a speedfunction model expressing a polishing speed, to calculate thickness ofthe thin film in the region after the polishing; a differencecalculating unit that calculates a difference between the calculatedthickness and an actual thickness of the thin film measured in theregion after the polishing; and a determining unit that determines anoptimum value for the parameters of the wiring width based on a resultof calculation by the difference calculating unit.

A polishing-condition predicting method according to still anotheraspect of the present invention is of predicting a polishing conditionby using a test substrate having a wiring groove formed in apredetermined shape, the polishing condition in polishing a thin filmformed on a substrate by a polisher. The polishing-condition predictingmethod includes receiving a possible value of parameters of a wiringwidth in a region of interest oh a thin film formed on the testsubstrate, the parameter values included in a groove depth functionmodel expressing a maximum depth at which a polisher enters into thegroove in the region; calculating a depth model value expressing a depthat which the polisher enters into the groove in the region and anadjacent region thereof by substituting the possible parameter anddimensional data of the wiring width into the groove depth functionmodel; calculating a pressure to be applied to the region bysubstituting the model values of the region and the adjacent region intoa pressure function model expressing pressure by height of the thin filmin each region; calculating thickness of the thin film in the regionafter the polishing by substituting the calculated pressure into a speedfunction model expressing a polishing speed; calculating a differencebetween the calculated thickness and an actual thickness of the thinfilm measured in the region after the polishing; and determining anoptimum value for the parameters of the wiring width based on a resultof calculation at the calculating a difference.

The other objects, features, and advantages of the present invention arespecifically set forth in or will become apparent from the followingdetailed description of the invention when read in conjunction with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic for explaining procedures of a large scaleintegration (LSI) fabrication process;

FIG. 2 is a schematic of a condition predicting apparatus according toan embodiment of the present invention;

FIG. 3 is a block diagram of the polishing-condition predictingapparatus;

FIG. 4 illustrates an outline of polishing condition predictionaccording to the embodiment;

FIG. 5 is a table showing one example of a measurement result of ablanket wafer;

FIG. 6 is a schematic for explaining one example of a TEG;

FIG. 7 is a schematic for explaining another example of the TEG havingmodules arranged in various wiring widths w and various wiring intervalss;

FIG. 8 is a table showing one example of a TEG measurement result;

FIG. 9 is a table showing one example of a data structure of an actualmeasurement database (DB);

FIG. 10 is a schematic for explaining a relationship between a depth ofa polishing pad entering a groove and a polishing pressure;

FIG. 11 illustrates an outline of polishing condition predictionaccording to the embodiment;

FIG. 12 is a table showing one example of a data structure of asimulation DB;

FIG. 13 is a flowchart of a polishing-condition prediction processperformed by the polishing-condition predicting apparatus; and

FIG. 14 is a flowchart of the polishing-condition prediction processperformed by the polishing-condition predicting apparatus.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Exemplary embodiments according to the present invention will beexplained in detail below with reference to the accompanying drawings.

First, a fabricating process in fabricating an LSI serving as asemiconductor device is schematically explained below. FIG. 1 is aschematic for explaining procedures of an LSI fabricating process. Asshown in FIG. 1, light is irradiated on an oxide film formed on asubstrate via a photo mask in fabricating an LSI, so that a wiringpattern is formed (shown in A in FIG. 1).

The photo mask is made of a material that does not transmit light onto atransparent glass substrate, and has a wiring pattern of a semiconductorcircuit depicted thereon. The wiring pattern of the semiconductorcircuit can be transferred onto the oxide film by irradiating anultraviolet ray onto the oxide film via the photo mask.

Next, a wiring groove is formed by etching the oxide film having thewiring pattern transferred thereonto (shown in B in FIG. 1). The etchingsignifies shaping the oxide film on the substrate by utilizing achemical reaction (i.e., a corrosion action) of a chemical agent or anion. Moreover, the wiring groove is adapted to form a wiring of thesemiconductor circuit. The wiring is made of copper having a highelectric conductivity or the like.

And then, copper plating is produced on the oxide film by electrolyticplating (shown in C in FIG. 1). The production of plating on the oxidefilm with copper to form the wiring is explained below. The electrolyticplating includes the reduction of a metallic ion by an electrolyticreaction and the deposition of metal on a conductive material of acathode.

Next, the copper plating produced on the oxide film is polished bychemical mechanical polishing (CMP) or the like, so that excessivecopper is removed (shown in D in FIG. 1). The CMP is a technique forgrinding and planarizing an uneven surface of the substrate by thecombined function of a chemical reaction and mechanical polishing by theuse of a chemical polishing agent and a polishing pad.

Upon completion of the polishing, another oxide film is formed on theoxide film having the wiring formed thereon (shown in E in FIG. 1). Inthe case of multiple wiring, a semiconductor circuit may be multiplyformed on one and the same substrate by repeating the series ofprocesses (shown in A to E in FIG. 1).

As the semiconductor device has become finer or has more wirings inrecent years, the uniform planarization of the oxide film (i.e., thesurface of the substrate) is required in the process of polishing thecopper plating (shown in D in FIG. 1) in the LSI fabrication. If thesurface of the substrate is not properly planarized, the wiring isshorted due to a contact between the wirings or the focus isinconveniently shifted in forming the wiring pattern, thereby causingreduction of yield.

According to the present invention, a polishing condition required foruniformly planarizing the surface of the substrate can be predicted byusing a simulation model that can predict variations of a polishingtime, a polishing pressure, and a polishing rotational speed. Inparticular, the polishing condition can be accurately predicted bytaking depth of the polishing pad entering into the groove in polishingthe copper plating, into consideration.

FIG. 2 is a block diagram of a polishing-condition predicting apparatusaccording to an embodiment of the present invention. A shown in FIG. 2,the polishing-condition predicting apparatus includes a centralprocessing unit (CPU) 201, a read-only memory (ROM) 202, a random-accessmemory (RAM) 203, a hard disk drive (HDD) 204, a hard disk (HD) 205, aflexible disk drive (FDD) 206, a flexible disk (FD) 207 as an example ofa removable recording medium, a display 208, an interface (I/F) 209, akeyboard 210, a mouse 211, a scanner 212, and a printer 213. Theseconstituents are connected to each other via a bus 200.

The CPU 201 is responsible for the control of the apparatus as a whole.The ROM 202 records a boot program and the like therein. The RAM 203 isused as work area of the CPU 201. The HDD 204 controls reading/writingdata from/to the HD 205 under the control of the CPU 201. The HD 205stores therein the data written under the control of the HDD 204.

The FDD 206 controls reading/writing data from/to the FD 207 under thecontrol of the CPU 201. The FD 207 stores therein the data written underthe control of the FDD 206 or allows the apparatus per se to read thedata stored therein.

Examples of the removable recording medium may include a compact discread-only memory (CD-ROM), a compact disc recordable (CD-R), a compactdisc rewritable (CD-RW), a magneto optical (MO) disk, a digitalversatile disk (DVD), and a memory card in addition to the FD 207. Thedisplay 208 is adapted to display thereon data such as a document, animage, and functional information in addition to a cursor, an icon, anda tool box. The display 208 may be a cathode ray tube (CRT), a thin-filmtransistor (TFT) liquid crystal display, a plasma display or the like.

The I/F 209 is connected to a network 214 such as the Internet via acommunication line, and further, is connected to other apparatuses viathe network 214. The I/F 209 is responsible for controlling the network214 and the interface therein, so as to control the input/output of thedata to/from an external device. The I/F 209 may be, for example, amodem or a local area network (LAN) adapter.

The keyboard 210 is provided with keys for use in inputting a character,a numeral, various kinds of instructions and the like, thereby inputtingthe data. The keyboard 210 may be an input pad of a touch panel type ora ten key pad. The mouse 211 moves a cursor, selects a range, moves awindow or varies a size. The mouse 211 may be a trackball or a joystickthat has a similar function as a pointing device.

The scanner 212 optically reads an image, and then, captures image datain the apparatus. Here, the scanner 212 may have an OCR function.Moreover, the printer 213 prints the image data or document data. Alaser printer or an ink jet printer, for example, can be adopted as theprinter 213.

FIG. 3 is a block diagram of the polishing-condition predictingapparatus according to the embodiment of the present invention. As shownin FIG. 3, the polishing-condition predicting apparatus includes aninput unit 301, a depth operating unit 302, a pressure calculating unit303, a thickness operating unit 304, a difference calculating unit 305,a determining unit 306, a condition input unit 307, and a conditiondetermining unit 308.

The polishing-condition predicting apparatus predicts a polishingcondition in polishing a thin film to be formed on a substrate to bedesigned by means of a polisher by using a test substrate having awiring groove formed into a predetermined shape. Specifically, thepolishing-condition predicting apparatus predicts the polishingcondition in polishing the thin film formed on the substrate to bedesigned by the CMP. The thin film formed on the substrate to bedesigned is made of, for example, copper or oxide. Here, the testsubstrate signifies a substrate for an evaluation such as a TEG havingwiring grooves formed into various shapes. The TEG is described later.

The input unit 301 receives an input of a possible parameter of a wiringwidth in an arbitrary region of interest included in a groove depthfunction model expressing a maximum depth of the polisher entering intothe groove in the region of interest on the thin film formed on the testsubstrate. Here, the arbitrary region of interest signifies an arbitraryfine region on the thin film formed on the test substrate.

In addition, the maximum depth of the polisher signifies a maximum depthat which the surface of the polisher (for example, polishing cloth) canenter in the groove in the region of interest during the polishing.Here, the groove depth function model is expressed by a mathematicalequation of the maximum depth of the polisher by the use of dimensionaldata of the polishing pressure applied onto the thin film during thepolishing, the relative speed between the thin film and the polisher,and the wiring width of the wiring groove formed on the test substrate.

The input unit 301 may receive inputs of possible parameters of thepressure applied onto the thin film formed on the test substrate and therelative speed between the thin film and the polisher, thereby using theparameters relevant to all of elements included in the groove depthfunction model.

The depth operating unit 302 substitutes the possible parameters inputby the input unit 301 and the dimensional data of the wiring width intothe groove depth function model, and then, operates a model valueexpressing the depth of the polisher entering into the groove in theregion of interest and a region around the region of interest.

Here, the possible parameter may be a specific numeric value, may fallwithin a variable range of the parameter, or may be a condition of thepossible parameter. For example, if a variable range of a parameter A isset to “0<A<100” and a condition is an “integer”, the parameter A cantake an integer from 1 to 99.

The dimensional data of the wiring width specifically signifiesdimensional data of the wiring width of the wiring groove formed on thetest substrate and an interval between adjacent wirings (i.e., wiringinterval). The dimensional data may be input from the input unit 301 ormay be recorded in the recording medium such as the HD 205 or the FD207.

Specifically, the depth operating unit 302 substitutes the dimensionaldata of the various parameters and various wiring widths into the groovedepth function model, thereby operating a model value according to thesubstituted parameter. That is to say, the depth operating unit 302operates various model values expressing the depth of the polisherentering into the groove in the region of interest and the region aroundthe region of interest by varying the substituted parameter.

The pressure calculating unit 303 substitutes the model values of theregion of interest and the region therearound operated by the depthoperating unit 302 into a pressure function model expressing a pressurein each of the regions by the height of the region concerned, therebycalculating a pressure to be applied to the region of interest.

The pressure function model expressing the pressure in each of theregions by the height of the region concerned is expressed by amathematical equation, in which a pressure in a certain region isrepresented by a difference in height from a peripheral region and adistance from the peripheral region.

The thickness operating unit 304 substitutes the pressure to be appliedto the region of interest calculated by the pressure calculating unit303 into a speed function model expressing a polishing speed inpolishing the thin film, thereby operating the thickness of the thinfilm in the region of interest after the polishing. The polishing speedduring the polishing is proportional to the pressure to be applied ontothe thin film and the relative speed between the surface of the thinfilm and the polisher.

As a consequence, the speed function model expressing the polishingspeed in polishing the thin film is represented by the pressure to beapplied onto the thin film and the relative speed between the surface ofthe thin film and the polisher. Specifically, a Preston expression, forexample, may be used as the speed function model. The thickness of thethin film signifies the height of the thin film from the surface of thesubstrate and the depth of the groove formed on the thin film.

The difference calculating unit 305 calculates a difference between thethickness of the thin film in the region of interest operated by thethickness operating unit 304 and an actually measured thickness of thethin film in the region of interest after the polishing. The actuallymeasured thickness of the thin film in the region of interest after thepolishing may be recorded in the form of a table in the recording mediumsuch as the HD 205 or the FD 207, thus to be read out only incalculating the difference from the result operated by the thicknessoperating unit 304.

Specifically, the difference calculating unit 305 calculates adifference between an actually measured thickness of the thin film inpositionally the same region on the test substrate as the region ofinterest, in which the thickness of the thin film is calculated by thethickness operating unit 304, that is, in a region having the samedimensional data on a wiring width and a wiring interval, and the resultoperated by the thickness operating unit 304. More specifically, thedifference calculating unit 305 compares the result operated by thethickness operating unit 304 with an actually measured result, and then,calculates a difference between the two results.

The determining unit 306 determines an optimum allowable one out of theparameters based on the result calculated by the difference calculatingunit 305. Specifically, the determining unit 306 may determine anoptimum parameter resulting from the operation by the depth operatingunit 302 when the result calculated by the difference calculating unit305 becomes minimum. In other words, since the difference is smallest atthe smallest result calculated by the difference calculating unit 305, aparameter at this time is regarded as an optimum parameter.

The condition input unit 307 receives an input of a possible parameterof the polishing condition in polishing the thin film formed on thesubstrate to be designed. The parameter relevant to the polishingcondition, for example, signifies the polishing pressure to be appliedonto the thin film formed on the substrate to be designed, the relativespeed between the surface of the thin film and the polisher, and thepolishing time.

Furthermore, the depth operating unit 302 substitutes the possibleparameter input by the condition input unit 307, the optimum valuedetermined by the determining unit 306, and the dimensional data of thewiring width in an arbitrary region of interest on the thin film formedon the substrate to be designed (hereinafter, “region of interest on asubstrate to be designed”) into the groove depth function model, therebyoperating model values expressing the depths of the polisher enteringinto the groove in the region of interest and the region around theregion of interest on the substrate to be designed.

Specifically, the depth operating unit 302 operates the model valuesexpressing the depths of the polisher entering into the groove in theregion of interest and the region around the region of interest on thesubstrate to be designed by using the optimum value determined by thedetermining unit 306 according to each of the parameters relevant to thepolishing condition input by the condition input unit 307.

Moreover, the pressure calculating unit 303 substitutes the model valuesin and around the region of interest on the substrate to be designed,which are operated by the depth operating unit 302, into the pressurefunction model, thereby calculating the pressure to be applied to theregion of interest on the substrate to be designed.

Additionally, the thickness operating unit 304 substitutes the pressureto be applied to the region of interest on the substrate to be designed,which is calculated by the pressure calculating unit 303, into the speedfunction model, thereby operating the thickness of the thin film in theregion of interest on the substrate to be designed.

In addition, the difference calculating unit 305 calculates thedifference between the thickness of the thin film in the region ofinterest on the substrate to be designed, which is calculated by thethickness operating unit 304, and a value set as the thickness of thethin film in the region of interest on the substrate to be designed.Specifically, the difference calculating unit 305 calculates thedifference between a value set as the thickness of the thin film inpositionally the same region on the substrate to be designed as theregion of interest on the substrate to be designed, in which thethickness of the thin film is calculated by the thickness operating unit304, and the operation result by the thickness operating unit 304.

The value set as the thickness of the thin film in the region ofinterest on the substrate to be designed signifies a desired thicknessof the thin film after the polishing, and it can be arbitrarily set.Furthermore, the value set as the thickness of the thin film in theregion of interest on the substrate to be designed may be input by theinput unit 301 or may be recorded in the recording medium such as the HD205 and the FD 207. Particularly, the thin film in the region ofinterest on the substrate to be designed may have, for example, a heightH on the substrate to be designed of 300±20 nanometers (nm) and a groovedepth of ±30 nm.

The condition determining unit 308 determines a possible parameter inputby the condition input unit 307 as the optimum parameter. Specifically,the condition determining unit 308 determines a possible parameter asthe optimum parameter based on the result calculated by the differencecalculating unit 305.

More specifically, the condition determining unit 308 may determine, asan optimum value, the parameter, based on which the depth operating unit302 performs the operation, when the result calculated by the differencecalculating unit 305 becomes minimum. In other words, the thin film canbe polished in a thickness most approximate to the thickness of the thinfilm in the region of interest on the substrate to be designed when theresult calculated by the difference calculating unit 305 becomesminimum, so that the parameter at this time is determined as the optimumvalue.

Incidentally, the CPU 201 executes a program recorded in the recordingmedium such as the ROM 202, the RAM 203, the HD 205 or the HD 207, shownin FIG. 2, thereby fulfilling their functions of the input unit 301, thedepth operating unit 302, the pressure calculating unit 303, thethickness operating unit 304, the difference calculating unit 305, thedetermining unit 306, the condition input unit 307, and the conditiondetermining unit 308, described above.

Next, the outline of polishing condition prediction according to theembodiment of the present invention is explained below. FIG. 4illustrates an outline of polishing condition prediction according tothe embodiment of the present invention.

<Calibration>

In predicting the polishing condition, a model parameter included in themodel function for use in a polishing simulation is extracted bycalibration, as shown in FIG. 4. The polishing simulation is adapted todetermine as to how the thin film is polished under a predeterminedpolishing condition by simulation. First, the polishing condition forthe calibration is set.

The polishing condition herein signifies a condition for polishing ablanket wafer and a TEG, described later. Specifically, the polishingcondition is determined based on the polishing time, the polishingpressure, and the polishing rotational speed. The polishing time, thepolishing pressure, and the polishing rotational speed can be set tovarious values, respectively. Furthermore, the polishing conditionincludes a condition for designating a region to be measured out of theTEG in TEG measurement, described later.

Subsequently, the polishing speed for each of the blanket wafers iscalculated. Here, the blanket wafer is a wafer for an evaluation, havinga thin film made of a single material (copper or oxide) over the entiresubstrate. The polishing speed with respect to each of the materials canbe calculated based on the measurement result after the blanket wafer ispolished under the polishing condition.

Specifically, the polishing speeds with respect to each of the materialsare calculated under the various polishing conditions (the polishingrotational speed and the polishing pressure), respectively, based on themeasurement result of the blanket wafer and the Preston equation(Equation 1). In Equation 1, reference character L designates apolishing quantity of a material to be polished (hereinafter, “thepolishing speed”); reference character η denotes a constant of each ofthe materials called a Preston constant; reference character Pdesignates a polishing pressure; reference character V denotes arelative speed (a contact relative speed between a polisher and amaterial to be polished); and reference character t designates apolishing time. Here, Equation 1 is equivalent to the speed functionmodel.L=ηPVt  (1)

The calculation of the polishing speed in a blanket wafer having acopper thin film formed thereon is explained in reference to FIG. 5.FIG. 5 is a table showing one example of the measurement result of theblanket wafer.

A table 500 of FIG. 5 shows measurement results (i.e., the heights H)when a blanket wafer having a thin film (i.e., copper plating) over theentire surface of a substrate is polished under various polishingconditions. The height H represents an absolute height from a mainsurface of a substrate (surface of a substrate having neither an oxidefilm nor copper plating formed thereon).

The constant η of each of the materials (copper) is obtained and thepolishing speed L is calculated by substituting the measurement resultshown in the table 500 to Equation 1. Here, the relative speed V inEquation 1 can be obtained based on, for example, the polishingrotational speed and the dimensional data on the polisher, such as apolishing pad. Specifically, a local relative speed V between apolishing pad and the thin film (i.e., copper plating) is obtained basedon the polishing rotational speed (i.e., rotational speed).

As a consequence, the polishing speeds L can be determined according tothe materials forming the thin films under the various polishingconditions, respectively. Particularly, a polishing quantity of thecopper plating ground for 1 minute under a certain polishing conditionbecomes a calculation result at a polishing speed L of 200 micron/min.

In the meantime, the height H of the copper plating and the groove depthS before and after the polishing are measured by using the TEG havingmodules arranged in various wiring widths and densities. The TEG is atest substrate for evaluation produced for the purpose of the evaluationof the material, basic design and basic process of the semiconductorcircuit or of check of a failure mechanism.

FIG. 6 is a schematic for explaining one example of the TEG. In the TEGshown in FIG. 6, the copper plating is formed on wiring patternsarranged in various wiring widths and densities. The height H of thecopper plating and the groove depth S are actually measured in thevarious wiring widths and densities by using the TEG.

A width between adjacent wiring grooves (i.e., an interval between thewirings) can be obtained based on the wiring width and density. Here, awiring interval is explained in a wiring width of 1 micrometer and awiring density of 75%. In this case, since the wiring density in acertain region is 75%, the ratio of the wiring width to the intervalbetween the wirings becomes 1:3. Based on this ratio, the intervalbetween the wirings can be expressed by an equation: 1×3=3 micrometers,that is, it becomes triple the wiring width.

Hereinafter, the TEG having the modules arranged in the various wiringwidths and densities. FIG. 7 is a schematic for explaining anotherexample of the TEG having the modules arranged in various wiring widthsw and various wiring intervals s. As shown in FIG. 7, the modules arearranged in the various wiring widths w and the various wiring intervalss on the TEG partitioned in a mesh-like manner.

In the meantime, wiring grooves are formed in the various wiring widthsw and the various wiring intervals s also in a region, in which nomodule is arranged on the TEG, covered with the copper plating. Andthen, the height H of the copper plating and the groove depth S on theTEG having the modules arranged thereon and the height H of the copperplating and the groove depth S between the modules are actually measuredunder the various polishing conditions (the polishing pressure, thepolishing rotational speed, and the polishing time), respectively.

FIG. 8 is a table showing one example of a TEG measurement result. InFIG. 8 actual measurement data on the height H of the copper plating onthe TEG and the groove depth S is shown. In other words, In FIG. 8 theactual measurement data on modules MOD1, MOD2, . . . arranged on the TEGand between the modules on the TEG is shown. The TEG measurement iscarried out before and after the polishing, thereby preparing the TEGmeasurement results shown in FIG. 8 according to the polishingconditions.

Next, an actual measurement DB relating to the TEG is created based onthe TEG measurement result and the TEG data. The TEG data is data in,for example, a GDSII format, and includes therein the dimensional data,such as a position, a wiring width and a wiring density on the TEG, onthe wiring pattern formed on the TEG.

FIG. 9 is a table showing one example of a data structure of the actualmeasurement DB. As shown in FIG. 9, the actual measurement data on theTEG partitioned in the mesh-like manner is stored in each of the meshesin the actual measurement DB. An area around the member to be polishedalso required to be accurately recognized to predict the polishingcondition required for uniformly polishing the surface of the substrate.In view of this, the TEG is partitioned in the mesh-like manner, therebypreparing the actual measurement data on each of the meshes.

In particular, the wiring width w, wiring interval s, height H andgroove depth S of each of the meshes are stored in the actualmeasurement DB. A position of each of the meshes on the TEG is expressedby coordinates (x, y).

The height H of the copper plating and the groove depth S in the actualmeasurement DB can be obtained from the TEG measurement result shown inFIG. 8. For example, the actual measurement data shown in FIG. 8 isassigned to the height H of the copper plating and the groove depth S ina mesh region corresponding to the module arranged on the TEG.Similarly, the actual measurement data shown in FIG. 8 is assigned tothe height H of the copper plating and the groove depth S in a regionbetween the modules.

Incidentally, the heights H of the copper plating and the groove depthsS in all of the regions partitioned in the mesh-like manner may beactually measured, and then, the actual measurement DB may be createdbased on the actual measurement result.

The wiring width w and the wiring interval s in the actual measurementDB may be obtained by using TEG data including the dimensional data onthe TEG, as shown in FIG. 6. Specifically, the wiring interval iscalculated based on the wiring width and the wiring density, asdescribed above, thereby determining an average wiring width and anaverage wiring interval. The resultant values are stored as the wiringwidth w and the wiring interval s in the actual measurement DB.

The actual measurement DB is created according to each of the polishingconditions, and includes the actual measurement data before and afterthe polishing. When there are a plurality of polishing steps since thethin film is made of a plurality of materials, the actual measurementdata before and after the polishing may be provided in each of thesteps. In this case, a model parameter may be adjusted in each of thesteps.

Subsequently, the calibration is carried out by using the model functionexpressing the pressure to be applied to each of the meshes on the TEGand the model function expressing the polishing pad entering in thegroove, thereby extracting optimum model parameters (A, α, β, γ, δ, andε, which will be described later) in obtaining the polishing condition.

The model function expressing the polishing pressure to be applied toeach of the meshes on the TEG is explained below. A polishing pressurePi applied to a region i on the TEG is represented by a value obtainedby adding a value expressing an influence by the height in a regionaround the region i to a polishing pressure Po applied to the entireTEG.

Namely, the polishing pressure Pi is expressed by Equation 2 below. InEquation 2, reference character A denotes a model parameter; referencecharacter h designates the height of the region; and reference characterf denotes a stress function. The stress function f is proportional to adistance between a region j and the region i, and therefore, it isexpressed by a Gauss function. The polishing pressure applied to each ofthe meshes on the TEG can be obtained based on Equation 2. Equation 2 isequivalent to the pressure function model.P _(i)=(A(h _(i) −Σf _(i−j)(h _(j)))+P _(o))  (2)

Next, the model function expressing the polishing pad entering in thegroove is explained below. As the model function expressing thepolishing pad entering in the groove is used αwβsγPδVε expressing amaximum depth, in which the polishing pad can be entering in the groove.The expression of the maximum depth, in which the polishing pad can beentering in the groove, is equivalent to the groove depth functionmodel.

Thereafter, the polishing is simulated by using the model functionexpressing the pressure to be applied to each of the meshes on the TEGand the model function expressing the polishing pad entering in thegroove, so that the grinding of the surface of the TEG is simulated(known technique: T. Tugbawa, Chip-Scale Modeling of PatternDependencies in Massachusetts Institute of Technology, 2002, Section 3).

The polishing simulation is specifically explained below. First, therelationship between the depth of the polishing pad entering in thegroove and the polishing pressure is explained. FIG. 10 is a schematicfor explaining the relationship between the depth of the polishing padentering in the groove and the polishing pressure. In FIG. 10, when, forexample, the depth of the polishing pad entering in the groove ismaximum, that is, is expressed by αwβsγPδVε, a pressure P2 applied tothe region j becomes “0” while the pressure P1 applied to the region ibecomes maximum. The region i corresponds to the region of interest: incontrast, the region j corresponds to the peripheral region.

In this manner, the polishing pressure in each of the regions on the TEGis obtained by using αwβsγPδVε expressing the maximum depth of thepolishing pad entering in the groove and Equation 2, and then, thepolishing speed L at each of the polishing pressures is calculated. As aconsequence, the polishing quantity in each of the regions (or meshes)on the TEG is obtained by integration based on the calculation result.

Next, the optimum model parameters A, α, β, γ, δ, and ε determining thepolishing condition are extracted based on the actual measurement valuesstored in the actual measurement DB and the polishing simulationresults.

For example, to match the actual measurement data after the polishingstored in the actual measurement DB with the polishing simulationresult, the model parameters A, a, β, γ, δ, and ε are variously changedwithin a predetermined range, and as a result, values with smallestdifferences are extracted as the optimum model parameters. A differencecalculating method includes a method for obtaining a root mean ofdifferences between the actual measurement data and the simulationresults at a plurality of typical points on the TEG (for example, themodules).

More specifically, the values P and V are first fixed, and then, theoptimum parameters are extracted by varying α, β, and γ by using theactual measurement DB (before and after the polishing) at two differentpolishing times. Next, the value V and the polishing time are fixed, andthen, δ is combined by using the actual measurement DB having twodifferent values P (after polishing). Finally, the values A and ε may beobtained.

The values A, α, β, γ, δ, and ε such extracted as described above andthe constant η of the polishing speed of each of the materials areregarded as the model parameters. When the thin film is formed on thesubstrate with a plurality of kinds of materials, the model parametersmay be obtained according to the number of steps since the polishingsteps are performed a plurality of times.

<Polishing Condition Predicting Simulation>

Next, the polishing condition prediction is simulated, thereby obtainingan optimum polishing condition. FIG. 11 illustrates an outline ofpolishing condition prediction according to the embodiment. Chip data ona chip to be simulated (for example, in a GDSII format) and a desiredheight and a desired groove depth of plating after the polishing arefirst prepared to simulate the polishing condition prediction.

And then, a simulation DB is created based on the chip data and aninitial thickness of the plating before the chip to be simulated. FIG.12 a table showing one example of the data structure of the simulationDB.

As shown in FIG. 12, the wiring width w and wiring interval s of thechip to be simulated, and the plating height H, and the groove depth Sin each of the regions partitioned in the mesh-like manner are stored inthe simulation DB.

The wiring width w and the wiring interval s stored in the simulation DBcan be obtained based on the information on the chip data, like inobtaining the wiring width w and the wiring interval s in the actualmeasurement DB, as described above. The plating height H expressing theinitial thickness of the plating before the polishing and the groovedepth S may be a value obtained based on a thickness predictingsimulation, in which a thickness of the thin film to be formed on thesubstrate is predicted, or may be an actually measured value.

A desired height of the plating and a desired groove depth after thepolishing can be arbitrarily set by a user. For example, the platingheight H in each of the regions may be set to 300±20 nm, and further,the groove depth of the plating may be set to ±30 nm.

Thereafter, the polishing simulation is carried out by using the datastored in the simulation DB, thereby predicting a plating height H and agroove depth S after the polishing. Specifically, the polishingsimulation is carried out by variously changing the polishing pressure,polishing rotational speed and polishing time included in the polishingconditions, thereby calculating a difference between the simulationresult (that is, the polishing prediction result) and the desired heightand groove depth. Here, the difference may be calculated by, forexample, using a root mean of differences between the polishingprediction results and the desired heights and groove depths in theregions on the chip.

In this manner, the polishing simulation is carried out under thevarious polishing conditions, thus searching the polishing conditionhaving a smallest difference, under which the optimum polishingprediction result can be produced. The polishing condition when thepolishing prediction result having the smallest difference is achievedis output as the optimum polishing condition.

Since the model parameters included in the model function used at thistime are values extracted by the calibration, the polishing simulationcan be carried out with substantially the actual measurement.

As described above, the polishing condition capable of obtaining thedesired height of the thin film formed on the substrate and the desiredgroove depth can be predicted by using the simulation model capable ofpredicting the variations in the polishing time, polishing pressure, andpolishing rotational speed. In particular, the height and groove depthof the thin film can be optimized in consideration of the polishing padentering into the groove in polishing the thin film, thus accuratelypredicting the polishing condition.

Subsequently, a polishing-condition prediction process performed in apolishing-condition predicting apparatus is explained in reference toFIGS. 13 and 14. FIG. 13 is a flowchart of a polishing-conditionprediction process that is performed in the polishing-conditionpredicting apparatus; and FIG. 14 is a flowchart of thepolishing-condition prediction process performed by thepolishing-condition predicting apparatus. The prediction of thepolishing condition in polishing the copper plating formed on thesubstrate is explained below. Here, the thickness signifies the heightof the copper plating formed on the substrate and the groove depth.

In the flowchart of FIG. 13, the polishing-condition predictingapparatus first judges as to whether the polishing condition forcalibration is set (step S1301). The polishing condition includes thepolishing pressure, the polishing rotational speed, and the polishingtime in polishing the TEG, which can be arbitrarily set, respectively.Moreover, the polishing condition set herein may one or two or more.

As soon as the polishing condition is set after waiting for the settingof the polishing condition (YES in step S1301), it is next judged as towhether the input of the possible parameter is accepted (step S1302). Inother words, the possible parameters are included in the variousfunction models for use in the polishing-condition prediction process.Here, the parameters include A, α, β, γ, δ and ε.

Furthermore, the possible parameter signifies a specific numeric valueor a condition for the possible parameter. The possible parameters maybe input one by one with respect to each of the parameters, or aparameter file or the like having various parameters described thereinmay be input.

In step S1302, as soon as the possible parameter is input after waitingfor the inputting of the possible parameter (YES in step S1302), thedepth entering in the groove at the copper plating surface in each ofthe meshes on the TEG is calculated (step S1303). That is to say, theentering depth is calculated by substituting the input possibleparameter (α, β, γ, δ and ε) and the polishing condition set in stepS1301 into the function model (αwβsγPδVε) expressing the maximum depthof the polishing pad entering into the groove.

More specifically, the dimensions w and s relating to the wiring widthat each of the meshes are specified based on the position of each of themeshes on the TEG. Thereafter, the entering depth is calculated bysubstituting the specified dimensions into the function model. Thedimensional data on the wiring width at each of the meshes on the TEG isacquired from, for example, the actual measurement DB shown in FIG. 9.

Thereafter, the polishing pressure to be applied to each of the meshesis calculated based on the operation result of each of the meshesoperated in step S1303 (step S1304). In particular, the polishingpressure to be applied to each of the meshes is calculated bysubstituting the depth entering in the groove at each of the meshes intoEquation 2, as expressed above.

Reference character h in Equation 2 is expressed by, for example, “h=H(see FIG. 9): the depth entering in the groove”. In other words, thepolishing pressure can be calculated by substituting the operationresult into Equation 2.

Subsequently, the thickness of the copper plating at each of the meshescan be operated by substituting the polishing pressure calculated instep S1304 into the function model expressing the polishing speed withrespect to the copper plating (step S1305). Specifically, the polishingquantity at each of the meshes is obtained based on the calculationresult calculated by substituting the polishing pressure to be appliedto each of the meshes into S1303 is determined as the optimum parameter.

In this manner, the optimum parameters included in the various functionmodels for use in predicting the polishing condition can be obtained.

Next, the processing when the polishing condition is predicted by usingthe determined optimum parameters is explained. In the flowchart of FIG.14, the polishing-condition predicting apparatus first determines as towhether the possible parameter relevant to the polishing condition inpolishing the copper plating formed on the substrate to be designed isinput (step S1401).

The input possible parameter relevant to the polishing conditionsignifies a value expressing the polishing condition in actuallypolishing the copper plating formed on the substrate to be designed. Aspecific parameter serving as a candidate of a polishing condition maybe input, or a searching range of the polishing condition may be input.

As soon as the possible parameter relevant to the polishing condition isinput after waiting for the inputting of the possible parameter (YES instep S1401), the depth of the surface of the copper plating enteringinto the groove at each of the meshes on the substrate to be designed iscalculated (step S1402). The entering depth is calculated bysubstituting the parameter relevant to the input polishing condition,that is, the parameters relevant to the polishing pressure and polishingrotational speed, and the optimum parameters determined in step S1307 ofFIG. 13 that is, the optimum parameters relevant to α, β, γ, δ and εinto the function model (αwβsγPδVε) expressing the maximum depth of thepolishing pad entering into the groove.

More specifically, the dimensions w and s relating to the wiring widthat each of the meshes are specified based Equation 1 and the polishingtime set in step S1301, thereby operating the thickness of the copperplating after the polishing.

Here, the function model expressing the polishing speed may be suchconfigured as to be read from the recording medium such as the HD 205and the FD 207 or to be input with the possible parameter in step S1302.Otherwise, the function model expressing the polishing speed may be suchconfigured that the variable η in the function model expressing thepolishing speed is calculated based on the table 500 shown in FIG. 5 anda process for determining the polishing speed is added.

Next, the difference between the thickness of the copper plating at eachof the meshes operated in step S1305 and the actually measured thicknessof the copper plating formed on the TEG after the polishing iscalculated (step S1306). For example, the difference is calculated bycomparing the thicknesses of the copper platings at the correspondingmeshes on the TEG with each other based on the actual measurement DBshown in FIG. 9.

In the difference calculating method, the root mean of the differences(or the differences) calculated at the meshes may be obtained. At thistime, the differences with respect to all of the meshes on the TEG arenot calculated, but a typical mesh on the TEG, for example, the moduleshown in FIG. 7 may be selected, so that a difference may be calculated.

Finally, the parameter with the minimum difference calculated in stepS1306 is determined as the optimum parameter (step S1307), thuscompleting a series of processings in this flowchart. Specifically, theparameter substituted into the function model expressing the maximumdepth of the polishing pad entering in the groove in step on theposition of each of the meshes on the substrate to be designed.Thereafter, the entering depth is calculated by substituting thespecified dimensions into the function model. The dimensional data onthe wiring width at each of the meshes on the substrate to be designedis acquired from, for example, the simulation DB shown in FIG. 12.

Thereafter, the polishing pressure to be applied to each of the meshesis calculated based on the operation result of each of the meshesoperated in step S1402 (step S1403). In particular, the polishingpressure to be applied to each of the meshes is calculated bysubstituting the depth entering in the groove at each of the meshes andthe optimum parameter A into Equation 2, as expressed above.

Reference character h in Equation 2 is expressed by, for example, “h=H(see FIG. 12): the depth entering in the groove”. In other words, thepolishing pressure can be calculated by substituting the operationresult into Equation 2.

Subsequently, the thickness of the copper plating at each of meshes canbe operated by substituting the polishing pressure calculated in stepS1403 into the function model expressing the polishing speed withrespect to the copper plating (step S1404). Specifically, the polishingquantity at each of the meshes is obtained based on the calculationresult calculated by substituting the polishing pressure to be appliedto each of the meshes into Equation 1 and the parameter relevant to thepolishing condition, that is, the parameter relevant to the polishingtime, input in step S1401, thereby operating the thickness of the copperplating after the polishing.

Here, the function model expressing the polishing speed may be suchconfigured as to be read from the recording medium such as the HD 205and the FD 207 or to be input with the possible parameter of thepolishing condition.

Next, the difference between the thickness of the copper plating at eachof the meshes operated in step S1404 and the desired thickness of thecopper plating formed on the substrate to be designed after thepolishing is calculated (step S1405). The desired thickness of thecopper plating formed on the substrate to be designed may be read fromthe values previously stored in the recording medium such as the HD 205and the FD 207 or may be input with the possible parameter relevant tothe polishing condition.

The desired thickness signifies, for example, the height H of the copperplating formed on the substrate to be designed of 300±20 nanometers orthe groove depth of the copper plating of ±30 nanometers. The differenceis calculated by comparing the thicknesses of the copper platings at thecorresponding meshes on the substrate to be designed with each otherbased on the simulation DB (after polishing) shown in FIG. 12.

In a difference calculating method, the root mean of the differences (ordifferences) calculated at the meshes may be used. At this time, thedifferences with respect to all of the meshes on the substrate to bedesigned are not calculated, but a typical mesh on the substrate to bedesigned, for example, the module shown in FIG. 7 may be selected, sothat a difference may be calculated. Otherwise, only the calculationresult satisfying the desired thickness, for example, out of thecalculated differences may be recorded in the recording medium such asthe HD 205 and the FD 207.

Finally, the parameter relevant to the polishing condition with theminimum difference calculated in step S1405 is determined as the optimumpolishing condition (step S1406), thus completing a series ofprocessings in this flowchart.

For example, when the possible parameter relevant to the polishingcondition input in step S1401 may take a plurality of values, all of thepossible parameters are subjected to the processing from step S1402 tostep S1405. Therefore, the differences under the various polishingconditions are calculated. After the differences with respect to all ofthe possible parameters are calculated, the parameter relevant to thepolishing condition with the smallest difference out of the calculationresults is determined as the optimum polishing condition.

In this manner, the polishing condition in polishing the copper platedsurface formed on the substrate to be designed can be predicted inconsideration of the variations of the polishing pressure, polishingrotational speed, and polishing time. Thus, the polishing-conditionpredicting apparatus according to the embodiment of the presentinvention can provide the polishing condition capable of polishing thecopper plating formed on the substrate to be designed in the desiredheight value and the desired groove depth or an approximate height andan approximate groove depth.

As described above, the polishing condition expressed by the height ofthe thin film formed on the substrate to be designed and the groovedepth by using the function model in consideration of the variations ofthe polishing time, polishing pressure, and polishing rotational speedcan be predicted by the polishing condition predicting program, therecording medium, the polishing-condition predicting apparatus and thepolishing condition predicting method.

In particular, the height of the thin film and the groove depth can beoptimized in consideration of the polishing pad entering into the groovein polishing the thin film, thereby predicting the polishing conditionmore accurately. Thus, the design period can be shortened, the worklabor can be alleviated, and further, the yield at the time of the LSIfabrication can be enhanced.

Furthermore, early appearance of a product of a good quality on themarket can produce a high advantage in securing a great share on themarket in fabricating a product at an initial stage from introduction togrowth.

Incidentally, the polishing-condition predicting apparatus according tothe embodiment can be implemented by executing a program prepared inadvance by a computer such as a personal computer or a work station.Such a program is recorded in a recording medium such as a hard disk, aflexible disk, a CD-ROM, an MO or a DVD that can be read by a computer,and therefore, is read from the recording medium by the computer, thusto be executed. In the meantime, such a program may be a transfer mediumthat can be distributed via a network such as the Internet.

According to the embodiments described above, it is possible shorten thedesign time, to reduce the work load, and to enhance yield at the timeof the LSI fabrication.

Although the invention has been described with respect to a specificembodiment for a complete and clear disclosure, the appended claims arenot to be thus limited but are to be construed as embodying allmodifications and alternative constructions that may occur to oneskilled in the art which fairly fall within the basic teaching hereinset forth.

1. A computer-readable recording medium that stores therein apolishing-condition predicting program for predicting a polishingcondition by using a test substrate having a wiring groove formed in apredetermined shape, the polishing condition in polishing a thin filmformed on a substrate by a polisher, the polishing-condition predictingprogram causing a computer to execute: receiving a possible value ofparameters of a wiring width in a region of interest on a thin filmformed on the test substrate, the parameter values included in a groovedepth function model expressing a maximum depth at which a polisherenters into the groove in the region; calculating a depth model valueexpressing a depth at which the polisher enters into the groove in theregion and an adjacent region thereof by substituting the possibleparameter and dimensional data of the wiring width into the groove depthfunction model; calculating a pressure to be applied to the region bysubstituting the model values of the region and the adjacent region intoa pressure function model expressing pressure by height of the thin filmin each region; calculating thickness of the thin film in the regionafter the polishing by substituting the calculated pressure into a speedfunction model expressing a polishing speed; calculating a differencebetween the calculated thickness and an actual thickness of the thinfilm measured in the region after the polishing; and determining anoptimum value for the parameters of the wiring width based on a resultof calculation at the calculating a difference.
 2. The computer-readablerecording medium according to claim 1, wherein the polishing-conditionpredicting program further causes the computer to execute receivingpossible values of parameters of the pressure applied on the thin filmof the test substrate and a relative speed between the thin film and thepolisher.
 3. The computer-readable recording medium according to claim1, wherein the determining includes determining a possible value fromwhich a smallest value is derived in calculation of the difference, asthe optimum value for the parameters of the wiring width.
 4. Thecomputer-readable recording medium according to claim 1, wherein thepolishing-condition predicting program further causes the computer toexecute: receiving a second possible value of parameters of thepolishing condition; calculating a depth model value expressing a depthat which the polisher enters into the groove in the second region and asecond adjacent region thereof on the substrate by substituting thesecond possible value, the optimum value determined at the determining,and dimensional data of a wiring width in a second region of interest onthe thin film on the substrate into the groove depth function model;calculating a second pressure to be applied to the second region bysubstituting the model value of the second region and the secondadjacent region, into the pressure function model; calculating a secondthickness of the thin film in the second region by substituting thesecond pressure into the speed function model; calculating a seconddifference between the second thickness and a value set as thickness ofthe thin film in the second region; and determining an optimum value forthe parameters of the polishing condition based on the seconddifference.
 5. The computer-readable recording medium according to claim4, wherein the parameters of the polishing condition includes parametersof the pressure to be applied on the thin film formed on the substrate,the relative speed between the surface of the thin film on the substrateand the polisher, and polishing time.
 6. The computer-readable recordingmedium according to claim 4, wherein the determining an optimum valuefor the parameters of the polishing condition includes determining apossible value from which a smallest value is derived in calculation ofthe second difference, as the optimum value for the parameters of thepolishing condition.
 7. A polishing-condition predicting apparatus thatpredicts a polishing condition by using a test substrate having a wiringgroove formed in a predetermined shape, the polishing condition inpolishing a thin film formed on a substrate by a polisher, thepolishing-condition predicting apparatus comprising: a receiving unitthat receives a possible value of parameters of a wiring width in aregion of interest on a thin film formed on the test substrate, theparameter values included in a groove depth function model expressing amaximum depth at which a polisher enters into the groove in the region;a depth calculating unit that substitutes the possible parameter anddimensional data of the wiring width into the groove depth functionmodel, to calculate a model value expressing a depth at which thepolisher enters into the groove in the region and an adjacent regionthereof; a pressure calculating unit that substitutes the model valuesof the region and the adjacent region into a pressure function modelexpressing pressure by height of the thin film in each region, tocalculate a pressure to be applied to the region; a thicknesscalculating unit that substitutes the calculated pressure into a speedfunction model expressing a polishing speed, to calculate thickness ofthe thin film in the region after the polishing; a differencecalculating unit that calculates a difference between the calculatedthickness and an actual thickness of the thin film measured in theregion after the polishing; and a determining unit that determines anoptimum value for the parameters of the wiring width based on a resultof calculation by the difference calculating unit.
 8. Thepolishing-condition predicting apparatus according to claim 7, whereinthe receiving unit further receives possible values of parameters of thepressure applied on the thin film of the test substrate and a relativespeed between the thin film and the polisher.
 9. The polishing-conditionpredicting apparatus according to claim 7, wherein the determining unitdetermines a possible value from which a smallest value is derived incalculation of the difference, as the optimum value for the parametersof the wiring width.
 10. The polishing-condition predicting apparatusaccording to claim 7, further comprising: a condition receiving unitthat receives a second possible value of parameters of the polishingcondition; and a condition determining unit that determines the secondpossible value as an optimum value for the parameters of the polishingcondition, wherein the depth calculating unit substitutes the secondpossible value, the optimum value determined by the determining unit,and dimensional data of a wiring width in a second region of interest onthe thin film on the substrate into the groove depth function model, tocalculate a model value expressing a depth at which the polisher entersinto the groove in the second region and a second adjacent regionthereof on the substrate, the pressure calculating unit substitutes themodel value of the second region and the second adjacent region, intothe pressure function model, to calculate a second pressure to beapplied to the second region, the thickness calculating unit substitutesthe second pressure into the speed function model, to calculate a secondthickness of the thin film in the second region, the differencecalculating unit calculates a second difference between the secondthickness and a value set as thickness of the thin film in the secondregion, and the condition determining unit determines an optimum valuefor the parameters of the polishing condition based on the seconddifference.
 11. The polishing-condition predicting apparatus accordingto claim 10, wherein the parameters of the polishing condition includesparameters of the pressure to be applied on the thin film formed on thesubstrate, the relative speed between the surface of the thin film onthe substrate and the polisher, and polishing time.
 12. Thepolishing-condition predicting apparatus according to claim 10, whereinthe condition determining unit determines a possible value from which asmallest value is derived in calculation of the second difference, asthe optimum value for the parameters of the polishing condition.
 13. Apolishing-condition predicting method of predicting a polishingcondition by using a test substrate having a wiring groove formed in apredetermined shape, the polishing condition in polishing a thin filmformed on a substrate by a polisher, the polishing-condition predictingmethod comprising: receiving a possible value of parameters of a wiringwidth in a region of interest on a thin film formed on the testsubstrate, the parameter values included in a groove depth functionmodel expressing a maximum depth at which a polisher enters into thegroove in the region; calculating a depth model value expressing a depthat which the polisher enters into the groove in the region and anadjacent region thereof by substituting the possible parameter anddimensional data of the wiring width into the groove depth functionmodel; calculating a pressure to be applied to the region bysubstituting the model values of the region and the adjacent region intoa pressure function model expressing pressure by height of the thin filmin each region; calculating thickness of the thin film in the regionafter the polishing by substituting the calculated pressure into a speedfunction model expressing a polishing speed; calculating a differencebetween the calculated thickness and an actual thickness of the thinfilm measured in the region after the polishing; and determining anoptimum value for the parameters of the wiring width based on a resultof calculation at the calculating a difference.
 14. Thepolishing-condition predicting method according to claim 13, furthercomprising receiving possible values of parameters of the pressureapplied on the thin film of the test substrate and a relative speedbetween the thin film and the polisher.
 15. The polishing-conditionpredicting method according to claim 13, wherein the determiningincludes determining a possible value from which a smallest value isderived in calculation of the difference, as the optimum value for theparameters of the wiring width.
 16. The polishing-condition predictingmethod according to claim 13, further comprising: receiving a secondpossible value of parameters of the polishing condition; calculating adepth model value expressing a depth at which the polisher enters intothe groove in the second region and a second adjacent region thereof onthe substrate by substituting the second possible value, the optimumvalue determined at the determining, and dimensional data of a wiringwidth in a second region of interest on the thin film on the substrateinto the groove depth function model; calculating a second pressure tobe applied to the second region by substituting the model value of thesecond region and the second adjacent region, into the pressure functionmodel; calculating a second thickness of the thin film in the secondregion by substituting the second pressure into the speed functionmodel; calculating a second difference between the second thickness anda value set as thickness of the thin film in the second region; anddetermining an optimum value for the parameters of the polishingcondition based on the second difference.
 17. The polishing-conditionpredicting method according to claim 16, wherein the parameters of thepolishing condition includes parameters of the pressure to be applied onthe thin film formed on the substrate, the relative speed between thesurface of the thin film on the substrate and the polisher, andpolishing time.
 18. The polishing-condition predicting method accordingto claim 16, wherein the determining an optimum value for the parametersof the polishing condition includes determining a possible value fromwhich a smallest value is derived in calculation of the seconddifference, as the optimum value for the parameters of the polishingcondition.